Detection of nitro-aromatics using C5N2 as an electrochemical sensor: a DFT approach

Nitroaromatics impose severe health problems and threats to the environment. Therefore, the detection of such hazardous substances is essential to save the whole ecosystem. Herein, the C5N2 sheet is used as an electrochemical sensor for the detection of 1,3-dinitrobenzene (1,3-DNB), trinitrotoluene (TNT), and picric acid (PA) using the PBE0/def2SVP level of theory as implemented in Gaussian 16. The highest interaction energy was observed for the picric acid@C5N2 complex. The trend in interaction energies for the studied system is PA@C5N2 >TNT@C5N2 >1,3-DNB@C5N2. The studied systems were further analysed by qualitative and quantitative analyses to determine the interactions between the nitroaromatic analytes and the C5N2 sheet. Electronic properties of all analytes@C5N2 complexes have been examined by NBO, EDD, FMO and DOS analysis. QTAIM analysis depicts the stronger non-covalent interactions for the PA@C5N2, which shows consistency with interaction energy and NCI analysis. Furthermore, NBO and FMO analyses show that the C5N2 substrate exhibits high sensitivity and selectivity towards the picric acid compared to TNT and 1,3-DNB nitroaromatics. EDD and DOS analyses are in agreement with NBO and FMO analyses. Furthermore, the recovery time of the studied system has been computed to determine the efficiency of C5N2 material as an electrochemical sensor. Overall, the results show that carbon nitride can be a good sensor for the detection of nitroaromatics.


Introduction
In recent years, extensive use of explosives in defence systems has raised serious concerns as they have potential negative impacts on human health and the whole ecosystem. 1Among these, nitroaromatics such as 1,3-dinitrobenzene (DNB), 2,4,6trinitrophenol, also known as picric acid (PA), and trinitrotoluene (TNT), have been widely used due to their highly explosive nature.][8] Therefore, detection of such toxic compounds is crucial to overcome their potential threats.
Various techniques such as HPLC, gas chromatography, 9 ion mobility spectrometry, [10][11][12] and capillary electrophoresis 13,14 have already been used for detection purposes.However, their non-specicity, difficulty in handling the instruments, presample processes, expensive instrumentations, and portability hinder their applicability as detectors. 15,16The demand for rapid, responsive, portable, and exible detecting systems marked the electrochemical sensors as a potential alternative for efficient detection. 17orous materials have gained signicant importance as electrochemical sensors due to their exceptional sensing properties 18 and various 2D and 3D substrates have been evaluated both experimentally and theoretically for this purpose.Such substances include fullerene, 19 metal-organic frameworks (MOFs), 20 aluminium nitride, 21 silicon carbide, 22 ZnO nanotubes, 23 silver-graphene quantum dots, 24 metal-doped graphene, 25,26 and covalent organic frameworks. 27In addition to these, graphene-polyaniline, 28 polyaniline/ZnO, 29 single-walled nanotubes, 30 multi-walled nanotubes, 31 polypyrrole, 32 and h-BN nanoclusters 33 have been used for detecting the chemical warfare agents (CWAs) including nitro explosives.Although these adsorbents are used to sense toxic agents, they lack certain characteristics, such as large surface area coupled with more active sites for adsorption, high porosity and reproducible results, required for the efficient performance of the adsorbents. 34ecently, carbon nitride became the heart of sensors due to its specic surface area and highly porous and chemically stable structure.Moreover, the intrinsic bandgap of carbon nitride proves its efficacy as a catalyst in water-splitting reactions, carbon dioxide reduction reactions, and degradation of organic pollutants. 35,36Numerous experimental and theoretical studies have been performed on the sensing capability of carbon nitride having different ratios of carbon and nitrogen, such as C 2 N, C 3 N 4, and C 4 N nanoakes. 37These materials show excellent sensing performance in the detection of toxic agents containing ammonia, hydrogen sulphides, 38 pesticides, 39 nitrogen halides, 40 neurotoxin hydrazine derivatives, 41 CWAs, 42,43 and nitro-explosives. 44,45n innovative form of carbon nitride, i.e.C 5 N 2, has not yet been explored for sensing.The C 5 N 2 material is synthesised through a condensation reaction between 1,2,4,5-benzene tetramine and hexaketocyclohexane. 46,47 Theoretical studies showed that C 5 N 2 is used as a catalyst to determine its stability and activity for the synthesis of hydrogen peroxide (H 2 O 2 ). 48oreover, C 5 N 2 is superior to the other carbon nitride forms due to its nanoporous crystalline structure with a narrow band gap (1.10 eV). 49These ndings motivated us to explore the sensing capability of the C 5 N 2 toward the nitroaromatic compounds, i.e., PA, 1,3-DNB and TNT.DFT calculations have been performed to determine the adsorption of the analytes on the C 5 N 2 surface.The selectivity and sensitivity of the analytes on the C 5 N 2 surface have been investigated by the FMO, NBO and DOS analyses.Furthermore, the nature of interactions is explored through the QTAIM and NCI analyses.

Computational methodology
Quantum chemistry computational calculations have been performed using Gaussian 16 B.01. 50 Structures of analystes, C 5 N 2 and complexes have been modelled using Gauss View soware. 51Geometries of the substrate C 5 N 2 and nitrocontaining analytes were optimised at the PBE0-D3BJ/def2-SVP level of theory.PBE0 is a hybrid DFT functional, which outperforms the pure DFT approach in computing molecular structures and properties throughout the periodic table. 52The literature has also backed the selection of PBE0 functional as it is widely applicable for molecular systems, providing accurate results for atomic energies, structural geometry, dissociation energies, and electronic and magnetic properties 53 and sensing interactions. 54PBE0/def2XVP has been used for adsorption studies of CO 2 , 55 metformin, 56 and different gases including H 2 , N 2 , CO, H 2 S, NH 3 , SO 2 , and CH 4 57 over graphitic carbon nitride and to study the non-covalent interactions between the decavanadate, arginine, and lysine side chains in proteins. 58Similarly, PBE0 has also been studied with different basis set combinations to study Se-doped graphitic carbon nitride (Se@gC 3 N 4 ) nanostructures used for the smart therapeutic delivery of zidovudine, 59 for the efficient sensing of glucose towards borophene, 53 functionalized carbon quantum dots for sensing curcumin, 60 and in studying the sensing of telomerase through semiconducting carbon nitrides. 61In a study about adsorption behaviour for efficient sensing of melamine through Mg 12 O 11 -X nanostructured materials, different hybrid functionals have been employed, and PBE0 has been reported to be ranked at the top in describing the sensing interactions. 54onsidering the long-range non-covalent interactions, Grimme's empirical D3 correction 62 with Becke-Johnston damping (D3BJ) 63 has been applied in all calculations.Multiwfn (version 3.80) 64 and VMD soware 65 have been used for qualitative and quantitative analyses.CYLview 66 has been employed to obtain high-resolution visualisation of modelled structures.
Analytes with different orientations on the C 5 N 2 sheet have been optimised to obtain the lowest energy structure of the complexes.These optimised structures are further validated via the vibrational frequency analysis, ensuring they have no imaginary frequency.The interaction energies of analytes with the sheet have been calculated through the following formula: DE int represents the interaction energy of the analyte@C 5 N 2 substrate, whereas the energy of complex, analyte, and C 5 N 2 sheet, respectively, are shown by the terms E analyte@C 5 N 2 , E analyte , and The interactions between the C 5 N 2 substrate and the nitro analytes have been thoroughly analyzed using Non-Covalent Interactions (NCI) analysis.This method primarily utilizes electron density (r) and the Reduced Density Gradient (RDG) to probe these interactions.The RDG is calculated using the following equation: 67 This equation indicates that the RDG value is inversely proportional to the electron density at a point.A higher electron density generally leads to a lower RDG value, suggesting a stronger potential for non-covalent bonding at that location.
Additionally, the electron density magnitude inuences these non-covalent interactions' strength.In contrast, the interaction's specic nature-whether repulsive or attractiveis determined by the Laplacian of the electron density (V 2 r).The Laplacian is expressed as the sum of its three eigenvalues from the Hessian matrix of electron density: 24 Among the eigenvalues derived from the Hessian matrix, the second eigenvalue (l 2 ) is especially important for determining the nature of the interactions within the molecule.Specically, a negative l 2 indicates strong, attractive interactions, such as those seen in hydrogen bonds, which are critical for molecular stability and function.Conversely, a positive l 2 points to repulsive interactions, which might indicate regions of molecular strain or steric clashes.Additionally, when l 2 is near zero, it typically signies the presence of weaker interactions, like van der Waals forces, which are essential for subtler molecular phenomena.
To visually capture and illustrate these different types of noncovalent interactions, we employ 2D RDG graphs and 3D isosurfaces generated using Multiwfn Soware (version 3.80). 64,68hese visualizations are color-coded to enhance understanding and interpretation: red represents repulsive interactions, blue denotes strong attractive interactions (notably hydrogen bonds), and green highlights the van der Waals interactions.This color-coding aids in quickly identifying the nature of interactions at a glance, providing an intuitive map of molecular interaction landscapes. 69urthermore, Quantum Theory of Atoms in Molecules (QTAIM) analysis has been performed to recognise the intramolecular and intermolecular interactions, particularly the non-covalent interactions. 70,71The nature and strength of intermolecular interactions between the nitroaromatic analytes and C 5 N 2 substrate are determined by the various topological parameters such as electron density (r), kinetic and potential energy density (G and V), total electron energy density (H), and Laplacian of the electron density (V 2 r), which exist at bond critical points (BCP) between nitroaromatic analytes and the substrate. 69 Generally, the values of potential energy density and kinetic energy density are always negative and positive, respectively.The sum of these two parameters (V and G) gives the total energy density (H).The values of H and V 2 r depict the type of interactions either covalent or non-covalent.If the value is H > 0 < V 2 r, then it shows the non-covalent interactions, while covalent interactions are depicted by the H < 0 > V 2 r. 71,72 Electronic density values further specify the strength of non-covalent interactions.If the value of electronic density is greater than 0.1, then it indicates the electrostatic attractive forces, while the presence of van der Waals interactions is indicated by the value of electronic density lower than 0.1. 73n addition, the electronic properties of the analytes@C 5 N 2 complexes have been determined at the same level of theory through frontier molecular orbital (FMO), electron density distribution (EDD), density of states (DOS) and natural bond orbital (NBO) analysis.The density of states validates the FMO analysis by better understanding the energy gap aer the adsorption of analytes.EDD plots of electronic density were obtained using Chemcra. 74Moreover, NBO charges are conrmed by providing visual aids through EDD plots to understand charge transfer upon complexation.Among the possible orientations of the 1,3-DNB complex (see Fig. S1 †), the most stable geometry occurred at the top of the pyrazine ring with an interaction energy of −23.21 kcal mole −1 .The benzene ring of the 1,3-DNB analyte was located on the site D while the two nitro groups were situated on the site B and E of the C 5 N 2 surface, respectively.For the TNT@C 5 N 2 complex, the analyte was placed in ve possible orientations on the C 5 N 2 sheet (see Fig. S3 †).Among these, the most stable geometry was obtained with an interaction energy of −31.64 kcal mole −1 where the analyte was oriented in between the C and D sites of the surface.The oxygen of TNT formed a hydrogen bond with the hydrogen pyrazine ring of C 5 N 2 substrate (2.49Å).The interaction energies of the possible orientation of analytes at C 5 N 2 are also presented in Table S1.† Stable geometries of 1,3-DNB@C 5 N 2 , TNT@C 5 N 2 and PA@C 5 N 2 have been shown in Fig. 2.

Results and discussion
Among all the three complex systems, picric acid interacts strongly with the surface of the substrate.For PA@C 5 N 2 complexes, the most stable geometry is obtained when the analyte is located on the top of the D site (pyrazine ring) with −34.37 kcal mole −1 of interaction energy.The other unstable optimized structures are presented in Fig. S2.† One of the reasons for such a high interaction energy is the formation of a hydrogen bond between the oxygen of picric acid and hydrogen of the pyrazine ring.The interaction energies of TNT@C 5 N 2 and PA@C 5 N 2 are stronger than those of the 1,3-DNB@C 5 N 2 complex due to the presence of hydrogen bond formation between the analyte and the substrate.Trends in interaction energies for the considered complexes are PA@C 5 N 2 > TNT@C 5 N 2 > 1,3-DNB@C 5 N 2 .The interaction energies along with bond lengths of all three complex systems have been presented in Table 1.

Quantum theory of atoms in molecules analysis
The nature of intermolecular interactions in nitroaromatics@C 5 N 2 complexes is analysed through the quantum theory of atoms in molecules (QTAIM) analysis.For the 1,3-DNB@C 5 N 2 complex, seven BCPs with four C-C, one C-N, one C-O, and one N-O were identied between the 1,3-DNB and C 5 N 2 substrate, as shown in Fig. 3.The value of Laplacian of electron density ranges from 0.019 to 0.033, signifying the noncovalent interactions, while electron density exhibits a value less than 0.1 (0.008 to 0.011), depicting the van der Waals interactions between the 1,3-DNB and C 5 N 2 sheet.Additionally, the remaining topological parameter values, i.e., H, G and V of 1,3-DNB@C 5 N 2 also indicate the presence of non-covalent interactions (Table S2 †).For the TNT@C 5 N 2 , eleven BCPs with two C-C, three C-N, two C-O, one C-H, one N-N, and two N-O were observed, as shown in Fig. 3. Topological parameters at the mentioned BCPs show non-covalent interactions between the TNT and C 5 N 2 substrate.The values of Laplacian and electron density range from 0.023 to 0.037 and 0.007 to 0.014, respectively.The remaining topological parameters, i.e., H, G and V of TNT@C 5 N 2 also indicated the presence of non-covalent interactions (see Table S1 †).
In the case of PA@C 5 N 2, ten BCPs are obtained with one O-H, two C-O, three C-C, two C-N, one N-N, and one N-O, between the picric acid and substrate (see Fig. 3).The topological parameters of PA@C 5 N 2 were similar to the TNT@C 5 N 2 except for the one O-H BCP.For all the BCPs, values of Laplacian and electron density range from 0.023 to 0.033 and 0.005 to 0.012, respectively.These topological values were in good agreement with the non-covalent interactions, particularly the van der Waals interactions.The value of electron density was highest for BCPs between the C8 of the picric acid and C18 of the C 5 N 2 surface which depicted the strong non-covalent interactions.The rest of topological parameters (H, G, V) also showed consistency with values of Laplacian and electron density as reported in Table 2.
Topological parameters for all considered complexes indicated the presence of non-covalent interaction between the analytes and the C 5 N 2 substrate.Values of electron density and Laplacian for PA@C 5 N 2 complexes showed van der Waals interactions along with hydrogen bond interactions.These QTAIM results are consistent with the interaction energies.

Non-covalent interaction analysis
The intermolecular interactions have been further characterised by the NCI analysis in the complexes of analytes-C 5 N 2 .It Fig. 2 The stable optimised structure of 1,3-DNB@C 5 N 2 , TNT@C 5 N 2 and picric acid@C 5 N 2 at PBE0-D3BJ/def2SVP level of theory.Interacting atoms of analytes and substrate have been shown by dotted lines.
Table 1 Interaction energies of all the complexes in kcal mol −1 along with bond length (Å) of interacting atoms of analytes and C 5 N 2 substrate Analyte@C 5 N  comprises of 2D RDG graph and 3D isosurfaces.Three color schemes have been used in 3D isosurface which describes the non-covalent interactions i.e., blue, green and red for attractive, weak van der Waals, and dispersive interactions between the analytes and substrate.Similarly, the 2D RDG graph shows attractive interactions in the form of hydrogen bonding (blue spikes), repulsive force (red spikes) and weak van der Waals forces (green spikes).Whereas the size of a particular patch is directly related to the strength of interactions.The larger the size of a particular patch, the greater will be the strength of that interaction.Similarly, values of electron density on the x-axis vary directly with the nature of interactions between the analytes and the substrate.
In the 3D isosurface, the presence of green isosurface between the analytes (1,3-DNB, TNT and PA) and the C 5 N 2 substrate conrms the weak van der Waals interactions consistent with the 2D RDG graph.Conversely, there is no hydrogen bond interaction between the analytes and substrate as revealed by the absence of clear blue patches. 75However, dispersed bluish-green spots in the case of TNT@C 5 N 2 and PA@C 5 N 2 showed more van der Waals interactions.2D RDG and 3D isosurface are presented in Fig. 4.Moreover, the presence of red spikes (0.01 to 0.03) in the 2D RDG graph represents the repulsive interaction that mostly exists between the atoms of aromatic rings of the C 5 N 2 substrate, also depicted in the 3D isosurface. 76In the case of picric acid@C 5 N 2 complex, the green isosurface and spikes in 3D and 2D graphs respectively, are dense and wide as compared to 1,3-DNB and TNT complexes, reecting more van der Waals interactions between the picric acid and C 5 N 2 which is also consistent with the interaction energies and QTAIM topological results.

Electronic properties: FMO and DOS analysis
Electronic properties of the substrate upon complexation have been studied through FMO analysis.Aer the analytes' adsorption, the substrate's conductivity signicantly changed, which inuenced its sensing capability.FMO analysis for the considered analytes@C 5 N 2 complexes has been performed.The energy values of HOMO, LUMO and their energy gaps have been reported in Table 3. Orbital density isosurface of all the analytes@complexes are shown in Fig. 5. Analysis shows that HOMO and LUMO values for pristine C 5 N 2 substrate are −3.42 eV and −2.82 eV respectively, which results in an energy gap of 0.60 eV.The energy gap of the pristine C 5 N 2 has been changed aer complexation with the analytes (1,3-DNB, TNT and PA).HOMO and LUMO energy values of 1,3-DNB@C 5 N 2 have been increased to −3.41 eV and −2.94 eV, respectively which results in decreased value of E H-L gap (0.47 eV).Aer adsorption of TNT analytes upon C 5 N 2 , the HOMO-LUMO energy gap reduces to 0.46 eV similar to the 1,3-DNB@C 5 N 2 complex.In this case, the Table 2 QTAIM topological parameters for PA@C 5 N 2 .Topological parameters are r (electron density), V2r (Laplacian of electron density), G (kinetic energy density), V (potential energy density) and H (total electron energy density) PA@C 5 N 2 decrease in E H-L gap is now attributed to the decreased value of both HOMO (−3.47 eV) and LUMO (−3.01 eV) as compared to the pristine C 5 N 2 substrate.Among all the studied systems, a signicant reduction in the HOMO-LUMO energy gap is observed in the case of PA@C 5 N 2 .The value of HOMO is reduced to −3.47 eV, comparable to the HOMO value of the pristine C 5 N 2 .However, pronounced shi in E H-L is mainly due to the reduction in the value of LUMO (−3.10 eV).This noticeable reduction in energy gap (0.37 eV) results in excellent conductivity and sensitivity of C 5 N 2 substrate towards the picric acid as compared to the other analytes (1,3-DNB and TNT).Orbital density patterns for considered analytes@C 5 N 2 complexes obtained through FMO analysis are shown in Fig. 5. Orbital density distribution shows similar patterns in all three analytes@C 5 N 2 complex systems.For all three systems (1,3-DNB@C 5 N 2 , TNT@C 5 N 2 , PA@C 5 N 2 ), the HOMO isosurface lies entirely on the sheet depicting the transfer of charge density from the C 5 N 2 surface aer adsorption of analytes.The LUMO density orbital is found half on the analyte and half on the substrate which shows a signicant reduction in the HOMO-LUMO energy gap.Among the 1,3-DNB@C 5 N 2 and TNT@C 5 N 2 complexes, PA@C 5 N 2 shows larger orbitals density isosurface, depicting the major shi in electronic density between C 5 N 2 and picric acid.This visual representation is analogous to the reduced HOMO-LUMO energy gap resulting in excellent sensitivity of picric acid toward the C 5 N 2 as compared to the rest of the analytes.
Electronic properties of considered complexes are further executed by the DOS analysis.The spectra of DOS are plotted in Fig. 6 for a better understanding of interactions aer adsorptions of analytes.Density of state spectra reveals that aer adsorption of analytes, virtual orbitals are shied more negatively, resulting in a reduced energy gap.In the DOS spectra, it is observed that HOMO appeared at −3.47 eV for PA@C 5 N 2 and TNT@C 5 N 2 as compared to pristine C 5 N 2 sheet (−3.42 eV) while the LUMO virtual orbitals are shied to −3.10 eV and −3.01 eV from −2.82 eV of C 5 N 2 , respectively.The formation of new orbitals of HOMO and LUMO results in a reduction of energy gap as compared to pristine substrate.A similar pattern is also observed for the 1,3-DNB@C 5 N 2 complex.Among the studied systems, the more pronounced shi is observed for the PA@C 5 N 2 system, thus lowering the energy gap.The shiing of orbitals and their peak intensities reect the conductivity and sensitivity of C 5 N 2 towards analytes, validating FMO results. 76

NBO and EDD analysis
Natural bond orbital (NBO) analysis provides a deeper evaluation of the interaction mechanism by determining the amount of charge transfer between the nitroaromatic analytes and C 5 N 2 substrate upon complexation.The NBO results of nitroaromatics@C 5 N 2 complexes are presented in Table 3.The values of NBO charges are negative on the 1,3-DNB, TNT and PA in nitroaromatics@C 5 N 2 complexes (presented in Table 3), which shows that charges are transferred from the sheet towards the nitroaromatics analytes.For the TNT@C 5 N 2 complex, 0.406 e charge is shied from the C 5 N 2 substrate to TNT.Similarly, 0.426 e charge is being transferred from substrate to PA in case of PA@C 5 N 2 complex while for 1,3-DNB@C 5 N 2 complex, the amount of charge transferred from substrate to the analyte is only 0.208 e.From these results, it is deduced that PA extracted the highest amount of charge from the C 5 N 2 substrate as compared to TNT and 1,3-DNB. 78lectron density difference (EDD) analysis helps to visualize the electronic density distribution among the nitroaromatics analytes and substrate upon complexation.The difference in the electronic density of the nitroaromatics@C 5 N 2 complex and the sum of the electronic density of the nitroaromatic analytes and C 5 N 2 substrate, taken separately, gives the EDD results. 44he EDD plots are given in the Fig. 7.In EDD plots, the transfer of electronic density is depicted by the orange (electronic density accumulated region) and pink (electronic density depleted region) colored isosurface, at the interacting sites of nitroaromatics and C 5 N 2 substrate.EDD results of 1,3-DNB@C 5 N 2 and TNT@C 5 N 2 show that nitroaromatics are mainly covered with orange isosurface, indicating the analytes withdraw electron density from C 5 N 2 substrate.In the EDD plot Table 3 HOMO-LUMO energies and their energy gap (eV) of all the three analytes-complexes and bare C 5 N 2 sheet along with NBO results

Analyte@C 5 N 2
Pristine C 5 N 2 PA@C 5 N 2 TNT@C 5 N 2  of picric acid@C 5 N 2 complex, the analyte is covered primarily with orange isosurface which depicts the shiing of electron density from pyrazine and benzene ring of C 5 N 2 , making them depleted region shown by pink color isosurface.The orange isosurface covering the phenolic group of picric acid along with three nitro groups signies strong extraction of electrons from the benzene ring of C 5 N 2 substrate as compared to TNT@C 5 N 2 and 1,3-DNB@C 5 N 2.These results show consistency with NBO analysis.

Recovery time
Recovery time is one of the parameters to determine the reproducibility of C 5 N 2 material as a sensor.Generally, thermal effects are applied to calculate the recovery time through transition state theory. 79The equation for calculating recovery time is as follows: The s stands for the recovery time, n represents the attempt frequency (10 14 s −1 ), 45,80,81 E ads express the adsorption energy, K denotes Boltzmann constant (1.99 × 10 −3 kcal mol −1 K −1 ), while T represents the temperature.For calculating the recovery time for the nitroaromatics@C 5 N 2 , different temperatures are employed.Generally, recovery time is directly proportional to interaction energies.Therefore, the recovery times for 1,3-DNB@C 5 N 2 , TNT@C 5 N 2 and PA@C 5 N 2 are, 5.24 × 10 −4 s, 4.10 s and 74.74 s, respectively at 473 K.The recovery time of the nitroaromatics@C 5 N 2 at different temperatures is presented in the Table S3.† It is observed that the systems' recovery time decreases with an increase in temperature. 81g. 6 DOS spectra of the pristine C 5 N 2 , PA@C 5 N 2 , TNT@C 5 N 2 and 1,3-DNB@C 5 N 2 .

Conclusion
DFT calculations have been employed to determine the sensing capability of C 5 N 2 substrate towards the lethal nitroaromatic compounds including 1,3-dinitrobenzene, trinitrotoluene and picric acid.Structures of nitroaromatics, C 5 N 2 sheet, and their complexes have been optimised at the PBE0-D3BJ/def2SVP level of theory.Nitroaromatics are placed at ve positions with different orientations to get the most stable geometry.Among studied systems, PA@C 5 N 2 is observed with high interaction energy of −34.37 kcal mol −1 .The trend in interaction is as follows: PA@C 5 N 2 > TNT@C 5 N 2 > 1,3-DNB@C 5 N 2 .Geometrical and electronic properties are determined for better understanding of the nature and type of interactions.QTAIM and NCI analyses conrm the existence of non-covalent interactions.The presence of denser green isosurface in 3D, along with bluishgreen spots in the 2D RDG graph, shows the strong noncovalent interactions in the PA@C 5 N 2 complex.These NCI results are veried by small and positive values of Laplacian and electronic density obtained through topological parameters.
The conductivity of C 5 N 2 has been increased aer the adsorption of analytes due to a reduction in the HOMO-LUMO gap.More signicant change is observed for PA@C 5 N 2 (0.37) which shows selectivity of C 5 N 2 towards the PA.FMO results are also conrmed by DOS analysis, which shows the prominent shiing of virtual orbital aer the adsorption of PA.Charge transfer (NBO) analysis also shows that among the studied systems, signicant charge transfer is observed for the PA@C 5 N 2 system.Furthermore, EDD analysis conrms the NBO analysis by providing visual illustrations.Recovery time for all the studied complexes has been computed using the transition state theory equation.The results of recovery time follow the interaction energies; however, recovery time could be appreciably reduced by increasing temperature.These results show that the C 5 N 2 substrate could be an efficient electrochemical sensor towards toxic nitroaromatics.

Fig. 1
Fig.1shows the optimised structure of C 5 N 2 used as an adsorbent.C 5 N 2 sheet consists of ve fused benzene rings, bridged by a pyrazine ring, consisting of four different kind of bonds, depending on the type of atoms and ring involved.The C-N bond length in the pyrazine ring is 1.36 Å whereas the bond length of three types of C-C bonds is 1.4 Å, 1.42 Å and 1.38 Å present in pyrazine, benzene and hydrogenated benzene rings, respectively.The analytes (1,3-DNB, TNT and PA) were placed on ve possible binding sites with different orientations to get the most stable ones.Such sites are labelled as A (in the central cavity of the sheet), B (forming a triangle with nitrogen atoms at the edges), C (top of the benzene ring), D (top of the pyrazine ring) and E (top of hydrogenated benzene ring).Analytes were positioned with possible orientations on the mentioned sites of the C 5 N 2 sheet to get the most stable geometry of the complex.Among the possible orientations of the 1,3-DNB complex (see Fig.S1 †), the most stable geometry occurred at the top of the pyrazine ring with an interaction energy of −23.21 kcal mole −1 .The benzene ring of the 1,3-DNB analyte was located on the site D while the two nitro groups were situated on the site B and E of the C 5 N 2 surface, respectively.For the TNT@C 5 N 2 complex, the analyte was placed in ve possible orientations on the C 5 N 2 sheet (see Fig.S3 †).Among these, the most stable geometry was obtained with an interaction energy of −31.64 kcal mole −1 where the analyte was oriented in between the C and D sites of the surface.The oxygen of TNT formed a hydrogen bond with the hydrogen pyrazine ring of C 5 N 2 substrate (2.49Å).The interaction energies of the possible orientation of analytes at C 5 N 2 are also presented in TableS1.† Stable geometries of 1,3-DNB@C 5 N 2 , TNT@C 5 N 2 and PA@C 5 N 2 have been shown in Fig.2.Among all the three complex systems, picric acid interacts strongly with the surface of the substrate.For PA@C 5 N 2 complexes, the most stable geometry is obtained when the analyte is located on the top of the D site (pyrazine ring) with −34.37 kcal mole −1 of interaction energy.The other unstable optimized structures are presented in Fig.S2.† One of the reasons for such a high interaction energy is the formation of a hydrogen bond between the oxygen of picric acid and hydrogen of the pyrazine ring.The interaction energies of TNT@C 5 N 2 and PA@C 5 N 2 are stronger than those of the 1,3-DNB@C 5 N 2 complex due to the presence of hydrogen bond formation between the analyte and the substrate.Trends in interaction energies for the considered complexes are PA@C 5 N 2 > TNT@C 5 N 2 > 1,3-DNB@C 5 N 2 .The interaction energies along

Fig. 1
Fig. 1 Optimised geometry of C 5 N 2 at PBE0-D3BJ/def2SVP with five binding sites i.e., central cavity (A), triazine site (B), benzene ring (C), hydrogenated benzene ring (D) and pyrazine ring (E).Blue color shows the nitrogen atom, grey shows the carbon atom and greyish-white shows the hydrogen.

Fig. 3
Fig. 3 Visual representation of BCPs via QTAIM analysis of the considered analytes@C 5 N 2 complexes.

Fig. 7
Fig. 7 EDD plots of nitroaromatics@C 5 N 2 complexes.The orange color isosurface shows the charge-accumulated region and the pink color isosurface represents the charge-depleted region.